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Nonlinear filters for linear models (a robust approach)
Liptser, R.Sh.; Runggaldier, W.J.;
Information Theory, IEEE Transactions on
Volume 41,
Issue 4,
July 1995
Page(s):1001
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1009
Abstract:
We consider the altering problem for linear models where the driving noises may be quite general, nonwhite and non-Gaussian, and where the observation noise may only be known to belong to a finite family of possible disturbances. Using diffusion approximation methods, we show that a certain nonlinear filter minimizes the asymptotic filter variance. This nonlinear filter is obtained by choosing at each moment, on the basis of the observations, one of a finite number of Kalman-type filters driven by a suitable nonlinear transformation of the “innovations”. As a byproduct we obtain also the asymptotic identification of the a priori unknown observation noise disturbance. By yielding an asymptotically efficient filter in face of an unknown observation noise, our approach may also be viewed as a robust approach to filtering for linear models
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